Attractors and repellors and failure of ciliary-beating frequency control in Chlamydomonas

Kenneth Foster1, Suphatra Adulrattananuwat1, Jureepan Saranak1, and Howard Blair2

1) Physics Department, Syracuse University, Syracuse, NY 13244-1130, USA 2) Depart. Elect. Eng. & Comp. Sci., Syracuse University, Syracuse, NY 13244-4100, USA

Physicists recently have taken a renewed interest in biological phenomena and as a consequence are introducing ideas from their field into biology. It is generally conceded that the behavior of even a single cell like Chlamydomonas is complex with independent control of the ciliary beating frequency, stroke velocity, phasing of the cilia, the ballistic/diffusive ratio, etc; seemingly a lot of control with seemingly few signalers. One model suggests behavioral response is like falling into a well (an "attractor" associated with that behavior where the spatial dimensions are made up of the influencing variables). This may be the case because relatively simple dynamical systems can exhibit more complex behaviors and dynamics than the underlying system by having associated networks of competing and reconfiguring attractors and repellors in the system's dynamics. Hence, one hypothesis for Chlamydomonas is that nature leverages this phenomenon such that the dynamics of the relatively simple control system contains a virtual complex system consisting of highly complex dynamically reconfigurable control networks of competing attractors and repellors that accounts for the organism's behavior. Attractors are usually associated with many feedback loops and we have already found evidence of two. We found that red light can stabilize the beating frequency to about 1% implying precise feedback control. However, when forced by modulating red light which excites photosynthesis and rapid changes in cell metabolites, the stability of ciliary beating is broken at 7 Hz in the increasing beating frequency direction and at 70 Hz in the decreasing direction implying two very rapid feedbacks. We will need dynamic ciliary and cell body measurements of cAMP, calcium ions, hydronium ions, redox potential, ATP, ADP, etc to elucidate the details of these hypothesized attractors. We hope that biologists with the requisite skills will join us in this effort.

e-mail address of presenting author: foster@phy.syr.edu